A227034 Composite numbers such that product_{i=1..k} (p_i/(p_i-1)) / sum_{i=1..k} (p_i/(p_i-1)) is an integer, where p_i are the k prime factors of n (with multiplicity).

4, 16, 72, 132, 256, 800, 1232, 2208, 2960, 5184, 5376, 11904, 19200, 23760, 39040, 41472, 65536, 72000, 76032, 76800, 84816, 203280, 259200, 288768, 332928, 345600, 373248, 383040, 416000, 614400, 628992, 640000, 663552, 691200, 1228800, 1996800, 2013312

Offset

1,1

Comments

All terms are even numbers.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..100

Example

Prime factors of 1232 are 2^4, 7, 11 and ((2/(2-1))^4*7/(7-1)*11/(11-1)) / (4*2/(2-1)+7/(7-1)+11/(11-1)) = 2.

Maple

with(numtheory); ListA226365:=proc(q) local a, d, n, p;
for n from 2 to q do if not isprime(n) then p:=ifactors(n)[2];
a:=mul((op(1, d)/(op(1, d)-1))^op(2, d), d=p)/add((op(1, d)/(op(1, d)-1))*op(2, d), d=p);
if type(a, integer) then print(n); fi; fi;
od; end: ListA226365(10^10);

Crossrefs

Cf. A224346, A224912, A226365, A227248.

Sequence in context: A231373 A161797 A124533 * A224660 A330610 A327541

Adjacent sequences: A227031 A227032 A227033 * A227035 A227036 A227037

Keyword

nonn

Author

Paolo P. Lava, Jul 03 2013

Status

approved